1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
nata0808 [166]
3 years ago
5

Find the area of the regular 18 gon with a radius of 13mm

Mathematics
1 answer:
pochemuha3 years ago
8 0
This polygon thing is all about triangles. If the polygon has 18 sides, it also has 18 central angles.  360/18  = 20.  This means that each one of the triangles has a vertex angle of 20.  We need to take this one triangle now and "pull" it out and isolate it cuz we only need to worry about 1, and we need to find the base measure of it for the perimeter, and the altitude of it for the apothem.  It would be easiest then to separate this triangle in half and have it be a right triangle, and the vertex angle is now 10.  If the vertex angle is 10 and this is a right triangle, then the 3rd angle by the triangle angle-sum theorem has to be 80.  The side ACROSS from the 80 degree angle is the apothem and the info telling us that the radius is 13 now puts that 13 as the hypotenuse of our right triangle.  We will use a trig identity relating this reference angle of 80 to the side across from it, "a", and the hypotenuse of 13.  sin(80)= \frac{x}{13} and we get that that side measures 12.8, rounded.  Now we have the apothem for the formula.  Now we need the base measure of the right triangle.  Use cos of 80 to find it: cos(80)= \frac{x}{13} ad we get the base measure of the right triangle is 2.25.  But don't forget that this is only half the original triangle we pulled out, so the base of the "whole" triangle is 2.25 * 2 which is 4.5.  If one side measures 4.5 and we have 18 of them, the perimeter for our formula is 81.  Now let's put everything together in the formula to find the area for the polygon: A= \frac{1}{2} (12.8)(81) and we find that the area is 518.4
You might be interested in
An assembly line produces 2 toasters per minute. It is 2:00pm and the line has finished 560 out of its goal of 900 for the day.
LenaWriter [7]

Answer:

I won't stop the line for a half hour break.

Step-by-step explanation:

<u>Proportions</u>

One quantity A is said to be proportional to other B if A can always be obtained by multiplying or dividing B by any constant number. Numbers {4,8,12} are proportional to {2,4,6} because they can be computed as twice their value

.

There is a situation described in the problem where we need to know if there will be enough time to produce the 900 toasters (the goal for the day) when the assembly line is stopped by half an hour.

Actual time: 2:00 pm

Final time: 5:00 pm

Rate of production: 2 toasters/minute

Actual production: 560 toasters

Updated goal: 900-560 = 340 toasters  

Those 340 toasters must be produced in the remaining 3 hours (180 minutes) of work. If the assembly line stops for half an hour (30 minutes), there will be only 150 minutes to finish the goal production. At a rate of 2 toasters/minute, there will be 2*150 = 300 toasters produced. But we need to produce 340 more toasters, so that break cannot be granted or we'll be 40 toasters under goal.

It the line keeps producing for 180 minutes, it would produce 2*180 = 360 toasters, 20 more than the goal.

Note: The maximum break time that can be granted is 20/2 = 10 minutes

4 0
3 years ago
Let f(x) = xe^-x+ ce^-x, where c is a positive constant. For what positive value of c does f have an absolute
Illusion [34]

Answer:

c=6

Step-by-step explanation:

The absolute maximum of a continuous function f(x) is where f'(x)=0. Therefore, we must differentiate the function and then set x=-5 and f'(x)=0 to determine the value of c:

f(x)=xe^{-x}+ce^{-x}

f'(x)=-xe^{-x}+e^{-x}-ce^{-x}

0=-(-5)e^{-(-5)}+e^{-(-5)}-ce^{-(-5)}

0=5e^{5}+e^{5}-ce^{5}

0=e^5(5+1-c)

0=6-c

c=6

Therefore, when c=6, the absolute maximum of the function is x=-5.

I've attached a graph to help you visually see this.

7 0
3 years ago
( 70 POINTS BRAINLIST) an offshore windmill is partly submerged in the ocean. it's tallest point is 120 meters above sea level i
alexdok [17]

Answer:

half of it would be 45

Step-by-step explanation:

120 - 30 = 90

90 divided by 2 = 45

hope this helped! sorry if i didn't answer your question, i was a little bit confused on what you wanted us to solve:)

if u want to find the length of it, it would be 150 because 120 + 30 = 150

7 0
2 years ago
Read 2 more answers
A 3-gallon bucket of paint costs $103.68. What is the price per cup?
prohojiy [21]

Answer:34.56

Step-by-step explanat 103.68 divded by 3 = 34.56

5 0
3 years ago
Solve the equation:<br><br> 3x + 34 when x = 4<br><br> Show work!
balandron [24]
3x + 34 

x = 4

Substitute x:

3 times 4 = 12

12 + 34 = 46

The answer is 46.

Hope this helped
4 0
3 years ago
Read 2 more answers
Other questions:
  • If there is 3/4 of pizza and it’s cut into 12/16 and everyone eats 2 slices how many slices are left
    9·1 answer
  • A glider descends 240 meters in 12 seconds. What is the average change in elevation?​
    8·1 answer
  • The amount of algae in a bloom, P, can be modeled by the equation P = t^4 + 6t^3+ 7t^2 + 8t, where t is measured in weeks. Durin
    8·2 answers
  • The car race lasted 0.004 hours. Convert this value into a fraction. hours
    8·1 answer
  • Danny has an unknown number of used cars at his
    10·2 answers
  • In a right triangle, the hypotenuse has endpoints P(–3, 2) and Q(1, –3). On a coordinate plane, line P Q has points (negative 3,
    11·2 answers
  • Find the zeros of the function.
    11·1 answer
  • 49of students at a school are boys. If there are 2610 students at the school, how many are girls?
    9·1 answer
  • Helppp!!!!!!!!!!<br><br> please
    13·2 answers
  • 7,14,15,9,11,14,11,10,17 what is the mode of the list of numbers?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!